Armies swamped by anguish or despair (6)
I believe the answer is:
hordes
'armies' is the definition.
(horde can mean an army)
'swamped by anguish or despair' is the wordplay.
'swamped by' indicates the answer is hidden within the clue.
'HORDES' can be found hidden inside 'anguish or despair'.
(Other definitions for hordes that I've seen before include "Bands" , ".Shored up with crowds" , "Vast multitudes" , "Horsed around with the multitudes" , "Huge noisy crowds" .)